Banzhaf power index (named after John F. Banzhaf III) is an index used to calculate the power (the ability to influence a group’s decision in a social or political setting, for example) of a voter in a group of coalition.
For example, a company where different people hold different percentage of sharesa or an electoral college where different states have different representatives leading to some members of the coalition having more influence in majority of the situation compared to others. Such a shareholder or voter or member is called a critical voter.
Source: A Mathematician Reads a Newspaper, Paulos